1. Combining several transformations
The order is very important
This power point will demonstrate which order to do them in
This will then be applied to a Sine Curve

2. Y= x2

3. Y= (2x)2
Horizontal stretch factor ½
HIVO HOVIS
Horizontal In side – Horizontal Opposite

4. Y= (x–3)2
Horizontal translation +3
HIVO HOVIS
Horizontal In side – Horizontal Opposite

5. More Combined Transformations
f(x) = (2x – 1)2
f(x) = (x)2
f(x) = (x–1)2
Step 1
Horizontal translation +1

6. More Combined Transformations
f(x) = (2x – 1)2
f(x) = (x–1)2
f(x) = (2x–1)2
Step 2
Horizontal stretch factor ½
All x values are ½ their original value
X intercept at x = ½ as expected if 2x–1 = 0 then x = ½

7. Y= (2x–3)2
Horizontal translation +3
Horizontal stretch factor ½

8. So the order is:
Translate horizontally left or right
Stretch horizontally
Stretch Vertically
Translate vertically
HIVO
Horizontal Inside Vertical Outside
HOVIS
Horizontal Opposite Vertical Is Same

9. We need to sketch the graph of y = 3sin(5t+90)+2
Trig Transformations y
y=sint t
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We need to sketch the graph of y = 3sin(5t+90)+2

10. Trig Transformations y
period = 360
y=sint t
Crosses x axis at 0, 180, 360, 540

11. Trig Transformations y
y=sin(t+90)
Translate horizontally left or right t
Horizontal translation of -90
Inside = horizontal opposite
Crosses x axis at 90, 270, 450

12. Trig Transformations y
Wave frequency = 5
Period =
= 72
y=sin(5t+90) 72 t
Stretch horizontally
Horizontal stretch of 
Inside = horizontal opposite
Crosses x axis at 18, 54, 90

13. Trig Transformations y
Stretch Vertically
y=3sin(5t+90) t
Vertical stretch of factor 3
Outside = vertical same

14. Trig Transformations y
y=3sin(5t+90)+2 t +2
Vertical translation of +2
Outside = vertical same

15. Sketch the graph of
y = 1sin(t + 45)
y = 2sin(t + 30)
y = 3sin(2t – 90)
y = 4sin(3t + 60)

16. y = 1sin(t + 45) y = 2sin(t + 30) 1 2 y = 3sin(2t – 90)
Translate horizontally by –30 Stretch vertically factor of 2
Translate horizontally by –45
y = 3sin(2t – 90)
y = 4sin(3t + 60) 3 4
Translate horizontally by +90 Stretch horizontally by ½ Stretch vertically factor of 3
Translate by horizontally –60 Stretch horizontally by 1/3 Stretch vertically factor of 4